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Show that |{:(a-b-c," "2a," "2a),(" "...

Show that `|{:(a-b-c," "2a," "2a),(" "2b,b-c-a," "2b),(" "2c," "2c,c-a-b):}|=(a+b+c)^(3)`

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`(a+b+c)^(3)`
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|(a-b-c,2b,2c),(2a,b-c-a,2c),(2a,2b,c-a-b)|=

Without expanding the determinant, prove that {:[( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) ]:} ={:[( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) ]:}

Show that |{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^3

Show that |(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^(3) .

Show that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=2|{:(a,b,c),(b,c,a),(c,a,b):}|

Show that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a)

Show that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a)

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-MATRICES -SOLVED PROBLEMS
  1. Show that |{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}| =(a-b)(b-c)(c-a)(a...

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  2. find determinant of |(1, omega, omega^(2)),(omega, omega^(2),1),(omega...

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  3. Show that |{:(a-b-c," "2a," "2a),(" "2b,b-c-a," "2b),(" "2c," "2...

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  4. Show that the determinant of skew - symmetric matrix of order three is...

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  5. Fiind the valueof x if: |{:(x-2, 2x-3, 3x-4),(x-4, 2x-9, 3x-16),(x-8...

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  6. Find the Adjoint and Inverse of the matrix A = [(1,2),(3,-5)]

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  7. Find the adjoint and the inverse of the matrix A=[{:(1,3,3),(1,4,3),(1...

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  8. Show that the matrix A=[{:(1,2,1),(3,2,3),(1,1,2):}] is non-singular a...

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  9. Find the rank of A=[{:(0,1,2),(1,2,3),(3,2,1):}] using elementary tran...

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  10. Find the rank of A=[{:(1,2,0,-1),(3,4,1,2),(-2,3,2,5):}] using element...

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  11. Apply the test of rank to examine whether the following equations are ...

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  12. Solve the following system of equations by using Cramer,s ruel . 3x...

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  13. Solve the equations 3x+4y+5z=18,2x+y+8z=13,5x-2y+7z=20 by matrix inver...

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  14. Solve the following system of equations by using Cramer,s ruel . 3x...

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  15. Solve the system of equations 2x+4y-z=0,x+2y+2z=5,3x+6y-7z=2 by Gauss ...

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  16. Solve the following- system of equations, 2x + 5y + 6z = 0, x - 3y + 8...

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  17. The number of nontrivial solutions of the system: x-y+z=0, x+2y=0, 2x+...

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  18. Theorem: Matrix multiplication is associative, i.e., if conformability...

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  19. Theorem : Matrix multiplication, is distri-butive over matrix addition...

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  20. If A is any matrix, then: (A^(T))^(T) =A

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